1 citations · 1 across the 10 of their papers we have counts for
10 papers
Permutation Equivariant Neural Networks for Symmetric Tensors
Edward Pearce-Crump
Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturall…
A Diagrammatic Approach to Improve Computational Efficiency in Group Equivariant Neural Networks
Edward Pearce-Crump, William J. Knottenbelt
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent charact…
Compact Matrix Quantum Group Equivariant Neural Networks
Edward Pearce-Crump
Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symme…
Graph Automorphism Group Equivariant Neural Networks
Edward Pearce-Crump, William J. Knottenbelt
Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph that has vertices, using the symmetric group $S_…
An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layers
Edward Pearce-Crump
The learnable, linear neural network layers between tensor power spaces of that are equivariant to the orthogonal group, , the special orthogonal group, $SO(…
Categorification of Group Equivariant Neural Networks
Edward Pearce-Crump
We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivar…
How Jellyfish Characterise Alternating Group Equivariant Neural Networks
Edward Pearce-Crump
We provide a full characterisation of all of the possible alternating group () equivariant neural networks whose layers are some tensor power of . In particula…
Connecting Permutation Equivariant Neural Networks and Partition Diagrams
Edward Pearce-Crump
Permutation equivariant neural networks are often constructed using tensor powers of as their layer spaces. We show that all of the weight matrices that appear in…
Brauer's Group Equivariant Neural Networks
Edward Pearce-Crump
We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of for three symmetry groups that ar…
A Multigraph Approach for Performing the Quantum Schur Transform
Edward Pearce-Crump
We take inspiration from the Okounkov-Vershik approach to the representation theory of the symmetric groups to develop a new way of understanding how the Schur-Weyl duality can be…